Real Numbers, Algebra, and Problem Solving Chapter 1 Real Numbers, Algebra, and Problem Solving

Real Number Sets Rational Numbers Irrational Numbers Discuss the difference between equal and approx (including notation)

Rational Numbers Integers Whole Numbers Natural Numbers

Real Numbers

Axioms for real numbers Closure For every real number a and b, a + b is a real number ab is a real number Commutative a + b = b + a ab = ba Associative For any numbers a, b and c, a + (b + c) = (a + b) + c a(bc) = (ab)c Distributive Property For every real number a, b, and c, a(b + c) = ab + ac Identity For any number a, a + 0 = a 1a = a Inverse For each number a, there is one and only one inverse, b, such that a + b = 0 For each nonzero number a, there is one and only one inverse, b, such that ab = 1

Unit Analysis Used to convert from one unit to another. How many seconds are in a week?

Computing with a calculator Use a calculator to evaluate each expression. Round to the nearest thousandth a. b. c. d. e. 6! – e2

Algebraic Expressions and Models Unit 1.2 Algebraic Expressions and Models

Numerical Expressions Numbers, operations, and grouping symbols Exponents ____________ 35 ___________________ Order of Operations P E MD AS

Math Vocabulary Give an example of each: Variable Algebraic Expression Term Coefficient Like terms Constant

1.3 and 1.4 Solving Linear Equations and Rewriting Equations and Formulas

Examples 3.5x – 2 = 5x - 8 -(x + 2) – 2x = -2(x + 1)

Word Problems You had to take your car to the shop and received a bill for $390. If the cost of parts was $215 and labor is $35/hour, how many hours did the repair take? Write an equation, then solve. A Retail sales manager earns $40,000 plus 5% of sales. If she earned $71,750 last year, what were her total sales?

Example 1. To solve C = 2п(r – 2) for r, what would you do first?

Example 2. Solve the formula A = wl for w

Example 3. Solve w = 3(x – 2) for x

Example 4. Solve the formula A = P + Prt for r

1.5 Problem Solving Using Algebraic models Understand the Problem Develop and carry out a Plan Find the Answer and Check ***Be sure to define any variables you use.

Example 1. A carpenter works one third as long after lunch as she worked before lunch. If she works a total of 8 hours, how long did she work before lunch?

Example 2. The giant economy size of Wheat Waffles is 25% larger than the regular size. The giant economy size is 500 grams. How large is the regular size?

Example The sum of two consecutive even integers is 50. What are the integers?

Useful Tips If two numbers are consecutive, call one x and the other x + 1 If two numbers are consecutive odd or consecutive even numbers, call one x and the other x + 2 If a number x is increased by n%, the new number is x(100% + n%) 2% increase… x(1.02)